Mousa Janini points out a requirement of bidirectional transactional replication:
The steps to create a Bi-directional replication is simple, and similar to the steps for configuring transnational replication with extra step to enable the @loopback_detection parameter of sp_addsubscription to ensure that changes are only sent to the Subscriber and do not result in the change being sent back to the Publisher.
The most common issue for the Bi-directional replication is when the loop back detection is not working as expected; which results in data conflicts and Primary Key Violations.
Read on to see what is the cause of this problem and what you can do to solve it.